Minimum value (2)

Calculus Level 3

What is point x x such that the value of f ( x ) f(x) below is minimum?

f ( x ) = ( x − 1 ) ( x ) ( x + 1 ) ( x + 2 ) \large f(x)=(x-1)(x)(x+1)(x+2)

2 \sqrt{2} 1 2 \frac{1}{2} − 1 ± 5 2 \frac{-1\pm\sqrt{5}}{2} 5 2 \frac{\sqrt{5}}{2} 1 ± 5 2 \frac{1\pm\sqrt{5}}{2}

Achmad Damanhuri by Achmad Damanhuri , 26, Indonesia

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1 solution

The function has three local extrima. At x=-(1/2), it has a maximum of 9/16 or 0.5625. At x=(-1+√5)/2 and x=(-1-√5)/2, it has minima of (-3+√5)/2 or -0.381966 each

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